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Deep learning has been widely applied in neuroimaging, including predicting brain-phenotype relationships from magnetic resonance imaging (MRI) volumes. MRI data usually requires extensive preprocessing prior to modeling, but variation introduced by different MRI preprocessing pipelines may lead to different scientific findings, even when using the identical data. Motivated by the data-centric perspective, we first evaluate how preprocessing pipeline selection can impact the downstream performance of a supervised learning model. We next propose two pipeline-invariant representation learning methodologies, MPSL and PXL, to improve robustness in classification performance and to capture similar neural network representations. Using 2000 human subjects from the UK Biobank dataset, we demonstrate that proposed models present unique and shared advantages, in particular that MPSL can be used to improve out-of-sample generalization to new pipelines, while PXL can be used to improve within-sample prediction performance. Both MPSL and PXL can learn more similar between-pipeline representations. These results suggest that our proposed models can be applied to mitigate pipeline-related biases, and to improve prediction robustness in brain-phenotype modeling.